We show that the global mixed gauge-gravitational anomaly of the worldvolume theory of the M5-brane vanishes, when the anomaly inflow from the bulk is taken into account. This result extends to the type IIA and heterotic E 8 E 8 five-branes. As a by-product, we provide a definition of the chiral fermionic fields for generic nonspin M5-brane worldvolume and determine the coupling between the self-dual field and the M-theory C-field.
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